A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

N Is a Number

Stage: 3 Challenge Level:

A group of N people
holidaying in the seaside town A decided to visit
their friends staying town B which is
N km (kilometres) along the coast.

Some of the group walk along the cliff path at a steady
N km an hour. The rest, one less in number than
the walkers, go by car which (not counting stops) averages $10$
times the speed of the walkers.

The road is much longer than the cliff path.

Those in the car stop for N minutes for fuel,
then N times as long as that for coffee, and are
further delayed for N minutes by a flock of sheep.
They finally reach town B one minute before the
walkers.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.